Why doesn't the remote desktop work? I think you should try and figure that out as that will be the best solution.

Are both machines on XP? Did you create a user account on your home PC for your work PC to connect to? Practice the setup method on a small (local) network if possible that way you don't have far to go between machines if you need to tweak a few settings.

BTW - Remote gaming on the net will be slow as buggery since a heap of data has to be transferred during visual apps. I tried something similar over a 100MBPs LAN connection and it was shyte.